W. H. Zurek, "Thermodynamiccost of computation, algorithmic complexity and the informa- tion metric','Nature341(6238),pp. 112-124(September1989)  Home/Search   Document Not in Database   Summary   Related Articles   Check

....by any error correction procedure that corrects errors perfectly. It would be interesting to see whether equality can be achieved in inequality (9.97) by error correction schemes that do not correct errors perfectly. 186 CHAPTER 9. ERROR CORRECTION AND MAXWELL S DEMON 9.7. 2 Discussion Zurek [205], Milburn [126] and Lloyd [117] have analyzed examples of quantum Maxwell demons, though not in the context of error correction. Lloyd notes that creation of new information in a quantum measurement is an additional source of inefficiency in his scheme, which involves measuring Z for a spin in ....

W. H. Zurek. Thermodynamic cost of computation, algorithmic complexity and the information metric. Nature, 341:119, 1989.

....depends on the observer s knowledge and is in general a non calculable quantity. A wellknown quantity in this context is the length of the shortest program generating the data as its output, the Kolmogorow complexity of the data. It can be proven that no algorithm can exist to calculate it (Zurek 1989). The proof relies on the Turing halting problem. Two classes of measures can be differentiated. First order or structural measures are maximal for completely random data sets and minimal for constant series. Second order or dynamical measures are small for regular as well as completely random ....

Zurek, W.H. (1989): Thermodynamic cost of computation, algorithmic complexity and the information metric. Nature 341, 119-124.

....did not obtain any further results on it. With respect to cognitive distance, we are not aware of further comparable work: all previous work involves ad hoc approaches, and no objective measure has been proposed [23] The closest in spirit, and most important stimulation, is the work of W. Zurek [25]. Since he does not provide a formal model, and charges costs in different ways in different places, we need to interpret his work in our model to obtain a proper comparison with our results. He established that the ultimate thermodynamic cost of erasure of a record x, provided the shortest ....

....must be given a program to do so to start out with. By definition the shortest such program has length K(yjx) Assume the computation from x to y produces g(x; y) garbage bits. Since the computation is reversible we can compute x from y and g(x; y) Consequently, jg(x; y)j K(xjy) by definition [25]. To end the computation with y alone we therefore must thermodynamically erase g(x; y) which is at least K(xjy) bits. 2 Together Claims 1, 2 prove the theorem. 2 Erasing a record x is actually a computation from x to the empty string ffl. Hence its thermodynamic cost is E(x; ffl) and given by ....

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W.H. Zurek. Thermodynamic cost of computation, algorithmic complexity and the information metric. Nature, 341:119--124, 1989.

....quickly. Complexity based on program length also allows one to define a quantity like Shannon s entropy for deterministic strings. This type of complexity measure will not be pursued further in this chapter, in part because it is not suitable for operational optimization. The reader is referred to [121, 150, 235], in addition to the references above, for details. Other computational models Let us note again that multiplicative complexity is reasonably wellsuited to computations that are completed through a sequence of calculations on current serial computing hardware. Another concrete computational model ....

W. H. Zurek. Thermodynamic cost of computation, algorithmic complexity and the information metric. Nature, 341(6238):119--124, September 1989.

....1961, Bennett, 1973, Bennett, 1982, Proc. PhysComp, 1981, 1992, 1994] In reference [Bennett et al. 1993] we and others developed a mathematical theory for the unavoidable number of irreversible bit operations in an otherwise reversible computation. A precursor to this line of thought is [Zurek, 1989]. Here we present the operational proof in [Li Vit anyi, 1994] for the known exact expression of the number of irreversible bit operations in an otherwise reversible computation proved differently in [Bennett et al. 1993] Many currently proposed physical schemes implementing adiabatic ....

....must be given a program to do so to start out with. By definition the shortest such program has length C(yjx) Assume the computation from x to y produces g(x; y) garbage bits. Since the computation is reversible we can compute x from y and g(x; y) Consequently, jg(x; y)j C(xjy) by definition [Zurek, 1989]. To end the computation with y alone we therefore must irreversibly erase g(x; y) which is at least C(xjy) bits. Together Claims 1, 2 prove the theorem. Corollary 5. Erasing a record x is actually a computation from x to the empty string ffl. Therefore, up to a logarithmic additive term, the ....

W.H. Zurek. Thermodynamic cost of computation, algorithmic complexity and the information metric. Nature, 341:119--124, 1989.

....can extend the notion of effective computations appropriately. In reference [Bennett et al. 1993] we and others developed a theory of information distance with application to the number of irreversible bit operations in an otherwise reversible computation. A precursor to this line of thought is [Zurek, 1989]. Among others, they considered the information distance obtained by minimizing the total amount of information flowing in and out during a reversible computation in which the program is not retained. Since the ultimate limit of energy dissipation by computation is expressed in the number of bits ....

....must be given a program to do so to start out with. By definition the shortest such program has length C(yjx) Assume the computation from x to y produces g(x; y) garbage bits. Since the computation is reversible we can compute x from y and g(x; y) Consequently, jg(x; y)j C(xjy) by definition [Zurek, 1989]. To end the computation with y alone we therefore must irreversibly erase g(x; y) which is at least C(xjy) bits. 2 Together Claims 1, 2 prove the theorem. 2 Erasing a record x is actually a computation from x to the empty string ffl. Hence its irreversibility cost is E(x; ffl) and given by a ....

W.H. Zurek. Thermodynamic cost of computation, algorithmic complexity and the information metric. Nature, 341:119--124, 1989.

....did not obtain any further results on it. With respect to cognitive distance, we are not aware of further comparable work: all previous work involves ad hoc approaches, and no objective measure has been proposed [25] The closest in spirit, and most important stimulation, is the work of W. Zurek [27]. Since he does not provide a formal model, and charges costs in different ways in different places, we need to interpret his work in our model to obtain a proper comparison with our results. He established that the ultimate thermodynamic cost of erasure of a record x, provided the shortest ....

W.H. Zurek. Thermodynamic cost of computation, algorithmic complexity and the information metric. Nature, 341:119--124, 1989.

....function: each state has an entropy, and the entropy change in going from state X to state Y by the most efficient process is simply the entropy difference between states X and Y . Thermodynamic ideas were first successfully applied to computation by Landauer. According to Landauer s principle [16, 4, 26, 27, 6] an operation that maps an unknown state randomly chosen from among n equiprobable states 29 onto a known common successor state must be accompanied by an entropy increase of log 2 n bits in other, non information bearing degrees of freedom in the computer or its environment. At room temperature, ....

....by Chaitin [7] on grounds of their similarity to conditional entropy in standard information theory. An analogous anti symmetric cost measure based on the difference of direct conditional complexities W 0 (yjx) K(xjy) Gamma K(yjx) was introduced and compared with W (xjy) by Zurek [26], who noted that the two costs are equal within a logarithmic additive term. Here we note that W 0 (yjx) is non transitive to a similar extent. Clearly, W 0 (yjx) is tied to the study of distance E 3 , the sum of irreversible information flow in and out of the computation. Namely, analysis of ....

W. H. Zurek. Thermodynamic cost of computation, algorithmic complexity and the information metric. Nature, 341:119--124, 1989.

....function: each state has an entropy, and the entropy change in going from state X to state Y by the most efficient process is simply the entropy difference between states X and Y . Thermodynamic ideas were first successfully applied to computation by Landauer. According to Landauer s principle [16, 4, 26, 27, 6] an operation that maps an unknown state randomly chosen from among n equiprobable states onto a known common successor state must be accompanied by an entropy increase of log 2 n bits in other, non information bearing degrees of freedom in the computer or its environment. At room temperature, ....

....advocated by Chaitin [7] on grounds of their similarity to conditional entropy in standard information theory. An analogous anti symmetric cost measure based on the difference of direct conditional complexities W 0 (yjx) K(xjy) Gamma K(yjx) was introduced and compared with W (xjy) by Zurek [26], who noted that the two costs are equal within a logarithmic additive term. Here we note that W 0 (yjx) is non transitive to a similar extent. Clearly, W 0 (yjx) is tied to the study of distance E 3 , the sum of irreversible information flow in and out of the computation. Namely, analysis of ....

W. H. Zurek. Thermodynamic cost of computation, algorithmic complexity and the information metric. Nature, 341:119--124, 1989.

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W. H. Zurek, "Thermodynamiccost of computation, algorithmic complexity and the informa- tion metric','Nature341(6238),pp. 112-124(September1989)

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Zurek, W. H., Thermodynamic cost of computation, algorithmic complexity and the information metric, Nature 341 119-124, 1989. To top 96

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W. H. Zurek. Thermodynamic cost of computation, algorithmic complexity and the information metric. Nature, 341:119--125, 1989.

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